Topology optimization for elasticity problem of isotropic and orthotropic materials based on the complex variable element-free Galerkin method

By using the improved complex variable moving least squares (ICVMLS) approximation to construct the shape function, thus the improved complex variable element-free Galerkin (ICVEFG) method is established for analyzing two types of topology optimization problems including isotropic and orthotropic materials in this study. Solid isotropic microstructure with penalization (SIMP) is utilized with relative density of nodes selected as the design variable, volume fraction set as the constraint and structural flexibility selected as the objective function, thus a mathematical model for topology optimization is developed, and the formula of sensitivity is derived. Four optimization examples of isotropic and orthotropic materials are given, and the feasibility of the ICVEFG method for solving topology optimization problem is demonstrated, in addition, the checkerboard phenomenon can be avoided; it is also shown that the ICVEFG method is more advantageous than the EFG method in solving orthotropic beam as well as isotropic problem with two fixed ends.